Wind energy is gradually growing with the increasing energy demand. However, the rising wind power penetration into modern grids could seriously affect the safe operation of power systems and power quality due to the intermittence and randomness of wind characteristics. Several effective ways could be considered to mitigate these issues: a robust power grid, energy storage, and wind power forecasting. Optimal integration of wind energy into power systems calls for high-quality wind power predictions. This research focuses on the short-term forecast of wind speed and power generation. Firstly, wind speed forecasting is studied. A case study is performed to analyze the forecasting performance of five approaches: the multivariate Facebook Prophet, seasonal autoregressive integrated with moving average (SARIMA), SARIMA with exogenous variable (SARIMAX), gated recurrent units (GRU) and long short-term memory (LSTM). The performance indicators are applied to verify the effectiveness of models, which are R-square (R2), mean square error (MSE), root mean square error (RMSE), and mean absolute error (MAE). The predictions obtained by the LSTM model almost coincide with the real-time wind speed, which is also supported by the performance indicators, which indicate that the LSTM model outperforms the other methods for the real-time dataset of IZTECH meteorological mast. The second part of the study is to forecast the wind power generation using the LSTM model and the wind speed forecasts and wind speed power curve of wind turbines in the wind farms. The proposed model is validated using the real-time wind power generation data from the EPIAS Transparency Platform. Due to the unavailable meteorological dataset, an ERA5 dataset of the location is used to predict wind speed and power generation. Also, each wind farm's daily forecasts are obtained to investigate the results for Day-ahead Market. The results indicate that using the LSTM model with the ERA5 dataset could give better forecasts than wind farms’ own forecasts. Additionally, it is understood that if the SCADA data could be obtained, the forecasting performance might be increased.